There are 500 employees in a firm, 45% are female.

14. There are 500 employees in a firm, 45% are female. A sample of 60 employees is selected randomly.
a. Determine the standard error of the proportion.
b. What is the probability that the sample proportion of females is between 0.40 and 0.55?
15. In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study.
a. What is the probability that the sample proportion of students living in the dormitories is between 0.172 and 0.178?
b. What is the probability that the sample proportion of students living in the dormitories is greater than 0.025?